.. _formatnmodl: NMODL ===== .. csv-table:: :header: "Name", "File extension", "Read", "Write" "NMODL", "``mod``", "✓", "✗" *NMODL* is a `DSL `_ for describing ion channel and synapse dynamics that is used by NEURON, which provides the mod2c compiler parses dynamics described in NMODL to generate C code that is called from NEURON. Arbor has an NMODL compiler, *modcc*, that generates optimized code in C++ and CUDA, which is optimized for the target architecture. NMODL does not have a formal specification, and its semantics are often ambiguous. To manage this, Arbor uses its own dialect of NMODL that does not allow some constructions used in NEURON's NMODL. .. note:: We hope to replace NMODL with a DSL that is well defined, and easier for both users and the Arbor developers to work with in the long term. Until then, please write issues on our GitHub with any questions that you have about getting your NMODL files to work in Arbor. This page is a collection of NMODL rules for Arbor. It assumes that the reader already has a working knowledge of NMODL. Units ----- Arbor doesn't support unit conversion in NMODL. This table lists the key NMODL quantities and their expected units. =============================================== =================================================== ========== quantity identifier unit =============================================== =================================================== ========== voltage v / v_peer mV temperature celsius °C diameter (cross-sectional) diam µm area (lateral) area µm² current_density (density mechanisms) identifier defined using ``NONSPECIFIC_CURRENT`` mA/cm² conductivity (density mechanisms) identifier inferred from current_density equation S/cm² e.g., in ``i = g*v`` g is the conductivity current (point and junction mechanisms) identifier defined using ``NONSPECIFIC_CURRENT`` nA conductance (point and junction mechanisms) identifier inferred from the current equation µS e.g., in ``i = g*v`` g is the conductance ion X current_density (density mechanisms) iX mA/cm² ion X current (point and junction mechanisms) iX nA ion X reversal potential eX mV ion X internal concentration Xi mmol/L ion X external concentration Xo mmol/L ion X diffusive concentration Xd mmol/L =============================================== =================================================== ========== Ions ----- * Arbor recognizes ``na``, ``ca`` and ``k`` ions by default. Any new ions used in NMODL need to be explicitly added into Arbor along with their default properties and valence (this can be done in the recipe or on a single-cell model). Simply specifying them in NMODL will not work. * The parameters and variables of each ion referenced in a ``USEION`` statement are available automatically to the mechanism. The exposed variables are: internal concentration ``Xi``, external concentration ``Xo``, reversal potential ``eX`` and current ``iX``. It is an error to also mark these as ``PARAMETER``, ``ASSIGNED`` or ``CONSTANT``. * ``READ`` and ``WRITE`` permissions of ``Xi``, ``Xo``, ``eX`` and ``iX`` can be set in NMODL in the ``NEURON`` block. If a parameter is writable, it is automatically readable and must not be specified as both. * If ``Xi``, ``Xo``, ``eX``, ``iX``, ``Xd`` are used in a ``PROCEDURE`` or ``FUNCTION``, they need to be passed as arguments. * If ``Xi`` or ``Xo`` (internal and external concentrations) are written in the NMODL mechanism, they need to be declared as ``STATE`` variables and their initial values have to be set in the ``INITIAL`` block in the mechanism. This transfers **all** responsibility for handling ``Xi`` / ``Xo`` to the mechanism and will lead to painted initial values being ignored. If these quantities are not made ``STATE`` they may be written to, but their values will be reset to their initial values every time step. * The diffusive concentration ``Xd`` does not share this semantics. It will not be reset, even if not in ``STATE``, and may freely be written. * ``Xd`` is present on all cables iff its associated diffusivity is set to a non-zero value. Special variables ----------------- Arbor exposes some read-only variables from the simulation to the NMODL mechanisms. These special variables must be added to the ``PARAMETER`` block to make them accessible. (This is different from NEURON where a built-in variable is declared ``ASSIGNED`` to make it accessible.) They are also reserved words and must not be used for other purposes. The list of special variables is: - ``v`` membrane voltage on current CV in mV, - ``diam`` CV diameter (cross-section) in µm, - ``area`` CV lateral (i.e., cylindrical mantle) surface area in µm², - ``celsius`` CV temperature in Celsius Variables declared by ``NONSPECIFIC_CURRENT`` or ``USEION ... READ ... WRITE ...`` should not be added to ``PARAMETER``, ``ASSIGNED`` or ``CONSTANT``. They are visible after their declaration and potentially writable. Both ``diam`` and ``celsius`` are set from the simulation side via the cell description. The CV surface area ``area`` is computed from the discretisation and the morphology. The membrane potential ``v`` can be written by a special ``VOLTAGE_PROCESS``. For all other mechanism kinds ``v`` is read-only and is evolved by Arbor through the cable model. Neither the timestep ``dt`` nor the current ``time`` are exposed to NMODL mechanisms. Functions, procedures and blocks -------------------------------- * ``SOLVE`` statements should be the first statement in the ``BREAKPOINT`` block. * The return variable of ``FUNCTION`` has to always be set. ``if`` without associated ``else`` can break that if users are not careful. * Any non-``LOCAL`` variables used in a ``PROCEDURE`` or ``FUNCTION`` need to be passed as arguments. This includes global variables like ``v``. Unsupported features -------------------- * Unit conversion is not supported in Arbor (there is limited support for parsing units, which are just ignored). * Unit declaration is not supported (ex: ``FARADAY = (faraday) (10000 coulomb)``). They can be replaced by declaring them and setting their values in ``CONSTANT``. * ``FROM`` - ``TO`` clamping of variables is not supported. The tokens are parsed, and reported through the ``mechanism_info``, but otherwise ignored. However, ``CONSERVE`` statements are supported. * ``TABLE`` is not supported, calculations are exact. * ``derivimplicit`` solving method is not supported, use ``cnexp`` instead. * ``VERBATIM`` blocks are not supported. * ``LOCAL`` variables outside blocks are not supported. * Free-standing blocks are not supported. * ``INDEPENDENT`` variables are not supported. * loops, arrays, and pointers are not supported by Arbor. Alternating normal and reaction statements in KINETIC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is not so much a feature as a bug that Arbor's ``modcc`` does not reproduce from NEURON. Given a file like: .. code-block:: NEURON { SUFFIX test_kinetic_alternating_reaction } STATE { A B C D } BREAKPOINT { SOLVE foobar METHOD sparse } KINETIC foobar { LOCAL x, y x = 23*v y = 42*v ~ A <-> B (x, y) x = sin(y) y = cos(x) ~ C <-> D (x, y) } one might expect that the reaction between ``C`` and ``D`` occurs with a rate proportional to ``sin(x)`` and ``cos(y)``. However, this file is equivalent to .. code-block:: NEURON { SUFFIX test_kinetic_alternating_reaction } STATE { A B C D } BREAKPOINT { SOLVE foobar METHOD sparse } KINETIC foobar { LOCAL x, y x = 23*v y = 42*v x = sin(y) y = cos(x) ~ A <-> B (x, y) ~ C <-> D (x, y) } which is almost never what the author would expect. Thus, this construction constitutes an error in ``modcc``; if want this particular behaviour, please state this explicitly by writing code similar to the second example. .. _arbornmodl: Arbor-specific features ----------------------- * It is required to explicitly pass 'magic' variables like ``v`` into procedures. It makes things more explicit by eliding shared and implicit global state. However, this is only partially true, as having ``PARAMETER v`` brings it into scope, *but only* in ``BREAKPOINT``. * Arbor's NMODL dialect supports the most widely used features of NEURON. It also has some features unavailable in NEURON, such as the ``POST_EVENT`` procedure block. This procedure has a single argument representing the time since the last spike on the cell. In the event of multiple detectors on the cell and multiple spikes on the detectors within the same integration period, the times of each of these spikes will be processed by the ``POST_EVENT`` block. Spikes are processed only once and then cleared. Example of a ``POST_EVENT`` procedure, where ``g`` is a ``STATE`` parameter representing the conductance: .. code:: POST_EVENT(t) { g = g + (0.1*t) } * Arbor allows a gap-junction mechanism to access the membrane potential at the peer site of a gap-junction connection as well as the local site. The peer membrane potential is made available through the ``v_peer`` variable, while the local membrane potential is available through ``v``, as usual. * Arbor offers a number of additional unary math functions which may offer improved performance compared to hand-rolled solutions (especially with the vectorized and GPU backends). All of the following functions take a single argument `x` and return a floating point value. ================== ======================================== ========= Function name Description Semantics ================== ======================================== ========= sqrt(x) square root :math:`\sqrt{x}` step_right(x) right-continuous heaviside step :math:`\begin{align*} 1 & ~~ \text{if} ~x \geq 0, \\ 0 & ~~ \text{otherwise}. \end{align*}` step_left(x) left-continuous heaviside step :math:`\begin{align*} 1 & ~~ \text{if} ~x \gt 0, \\ 0 & ~~ \text{otherwise}. \end{align*}` step(x) heaviside step with half value :math:`\begin{align*} 1 & ~~ \text{if} ~x \gt 0, \\ 0 & ~~ \text{if} ~x \lt 0, \\ 0.5 & ~~ \text{otherwise}. \end{align*}` signum(x) sign of argument :math:`\begin{align*} +1 & ~~ \text{if} ~x \gt 0, \\ -1 & ~~ \text{if} ~x \lt 0, \\ 0 & ~~ \text{otherwise}. \end{align*}` exprelr(x) smooth continuation over :math:`x=0` of :math:`x/(e^x - 1)` sigmoid(x) sigmoidal function :math:`\frac{1}{1+e^{-x}}` relu(x) rectified linear function :math:`max(0, x)` tanh(x) hyperbolic tangent :math:`tanh(x)` ================== ======================================== ========= .. _formatnmodl_voltageproc: Voltage Processes ----------------- Some cases require direct manipulation of the membrane voltage ``v``; which is normally prohibited and for good reason so. For these limited applications, however, we offer mechanisms that are similar to the ``density`` mechanism, but are tagged with ``VOLTAGE_PROCESS`` where normally ``SUFFIX`` would be used. This is both a very sharp tool and a somewhat experimental feature. Depending on our experience, it might be changed or removed. Using a ``VOLTAGE_PROCESS``, voltage clamping and limiting can be implemented, c.f. relevant examples in the ``default`` catalogue. Example: limiting membrane voltage from above and below .. code:: none NEURON { VOLTAGE_PROCESS v_limit GLOBAL v_low, v_high } PARAMETER { v_high = 20 (mV) v_low = -70 (mV) } BREAKPOINT { v = max(min(v, v_high), v_low) } As of the current implementation, we note the following details and constraints * only the ``INITIAL`` and ``BREAKPOINT`` procedures are called. * no ``WRITE`` access to ionic quantities is allowed. * only one ``VOLTAGE_PROCESS`` may be present on a single location, adding more results in an exception. * the ``BREAKPOINT`` callback will execute _after_ the cable solver. A consequence of this is that if the initial membrane potential :math:`V_0` is unequal to that of a potentially applied voltage clamp :math:`V_c`, the first timestep will observe :math:`V_0`. .. _format-sde: Stochastic Processes -------------------- Arbor supports :ref:`stochastic processes ` in the form of stochastic differential equations. The *white noise* sources can be defined in the model files using a ``WHITE_NOISE`` block: .. code:: none WHITE_NOISE { a b c } Arbitrary white noise variables can be declared (``a, b, c`` in the example above). The noise will be appropriately scaled with the numerical time step and can be considered unitless. In order to influence the white noise generation, a seed value can be set at the level of the simulation through the optional constructor argument ``seed`` (see :ref:`here ` or :ref:`here `). If the state is updated by involving at least one of the declared white noise variables the system is considered to be stochastic: .. code:: none DERIVATIVE state { s' = f + g*a } The solver method must then accordingly set to ``stochastic``: .. code:: none BREAKPOINT { SOLVE state METHOD stochastic } Nernst ------ Many mechanisms make use of the reversal potential of an ion (``eX`` for ion ``X``). A popular equation for determining the reversal potential during the simulation is the `Nernst equation `_. Both Arbor and NEURON make use of ``nernst``. Arbor implements it as a mechanism and NEURON implements it as a built-in method. However, the conditions for using the Nernst equation to change the reversal potential of an ion differs between the two simulators. 1. In Arbor, the reversal potential of an ion remains equal to its initial value (which has to be set by the user) over the entire course of the simulation, unless another mechanism that alters that reversal potential (such as ``nernst``) is explicitly selected for the entire cell. (see :ref:`cppcablecell-revpot` for details). .. NOTE: This means that a user cannot indicate to use ``nernst`` to calculate the reversal potential on some regions of the cell, while other regions of the cell have a constant reversal potential. It's either applied on the entire cell or not at all. This differs from NEURON's policy. 2. In NEURON, there is a rule which is evaluated (under the hood) per section of a given cell to determine whether or not the reversal potential of an ion remains constant or is calculated using ``nernst``. The rule is documented `here `_ and can be summarized as follows: Examining all mechanisms in a given section, if the internal or external concentration of an ion is **written**, and its reversal potential is **read but not written**, then the Nernst equation is used **continuously** during the simulation to update the reversal potential of the ion. And if the internal or external concentration of an ion is **read**, and its reversal potential is **read but not written**, then the Nernst equation is used **once** at the beginning of the simulation to calculate the reversal potential of the ion and then remains constant. Otherwise, the reversal potential is set by the user and remains constant. One of the main consequences of this difference in behavior is that in Arbor, a mechanism modifying the reversal potential (for example ``nernst``) can only be applied (for a given ion) at a global level on a given cell. While in NEURON, different mechanisms can be used for calculating the reversal potential of an ion on different parts of the morphology. This is due to the different methods Arbor and NEURON use for discretising the morphology. (A ``region`` in Arbor may include part of a CV, whereas in NEURON, a ``section`` can only contain full ``segments``). Modelers are encouraged to verify the expected behavior of the reversal potentials of ions as it can lead to vastly different model behavior. .. _formatnmodl-faster: Tips for Faster NMODL --------------------- .. Note:: If you are looking for help with NMODL in the context of NEURON this guide might not help. NMODL is a language without formal specification and many unexpected characteristics (many of which are not supported in Arbor), which results in existing NMODL files being treated as difficult to understand and best left as-is. This in turn leads to sub-optimal performance, especially since mechanisms take up a large amount of the simulations' runtime budget. With some understanding of the subject matter, however, it is quite straightforward to obtain clean and performant NMODL files. We regularly have seen speed-ups factors of roughly three from optimising NMODL. First, let us discuss how NMODL becomes part of an Arbor simulation. NMODL mechanisms are given in ``.mod`` files, whose layout and syntax have been discussed above. These are compiled by ``modcc`` into a series of callbacks as specified by the :ref:`mechanism_abi`. These operate on data held in Arbor's internal storage. But, ``modcc`` does not generate machine code, it goes through C++ (and/or CUDA) as an intermediary, which is processed by a standard C++ compiler like GCC (or nvcc) to produce either a shared object (for external catalogues) or code directly linked into Arbor (the built-in catalogues). Now, we turn to a series of tips we found helpful in producing fast NMODL mechanisms. In terms of performance of variable declaration, the hierarchy is from slowest to fastest: 1. ``RANGE ASSIGNED`` -- mutable array 2. ``RANGE PARAMETER`` -- configurable array 3. ``ASSIGNED`` -- mutable 4. ``PARAMETER`` -- configurable 5. ``CONSTANT`` -- inlined constant ``RANGE`` ~~~~~~~~~ Parameters and ``ASSIGNED`` variables marked as ``RANGE`` will be stored as an array with one entry per CV in Arbor. Reading and writing these incurs a memory access and thus affects cache and memory utilisation metrics. It is often more efficient to use ``LOCAL`` variables instead, even if that means foregoing the ability to re-use a computed value. Compute is so much faster than memory on modern hardware that re-use at the expense of memory accesses is seldom profitable, except for the most complex terms. ``LOCAL`` variables become just that in the generated code: a local variable that is likely residing in a register and used only as long as needed. ``PROCEDURE`` ~~~~~~~~~~~~~ Prefer ``FUNCTION`` over ``PROCEDURE``. The latter *require* ``ASSIGNED RANGE`` variables to return values and thus stress the memory system, which, as noted above, is not most efficient on current hardware. Also, they may not be inlined, as opposed to a ``FUNCTION``. ``PARAMETER`` ~~~~~~~~~~~~~ ``PARAMETER`` should only be used for values that must be set by the simulator. All fixed values should be ``CONSTANT`` instead. These will be inlined by ``modcc`` and propagated through the computations, which can uncover more optimisation potential. Sharing Expressions Between ``INITIAL`` and ``BREAKPOINT`` or ``DERIVATIVE`` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This is often done using a ``PROCEDURE``, which we now know is inefficient. On top, this ``PROCEDURE`` will likely compute more outputs than strictly needed to accomodate both blocks. DRY code is a good idea nevertheless, so use a series of ``FUNCTION`` instead to compute common expressions. This leads naturally to a common optimisation in H-H style ion channels. If you heeded the advice above, you will likely see this pattern emerge: .. code:: na = n_alpha() nb = n_beta() ntau = 1/(na + nb) ninf = na*ntau n' = (ninf - n)/ntau Written out in this explicit way, it becomes obvious that this can be expressed compactly as .. code:: na = n_alpha() nb = n_beta() nrho = na + nb n' = na - n*nrho The latter code is faster, but neither ``modcc`` nor the external C++ compiler will perform this optimisation [#]_. This is less easy to see when partially hidden in a ``PROCEDURE``. .. [#] GCC/Clang *might* attempt it if asked to relax floating point accuracy with ``-ffast-math`` or ``-Ofast``. However, Arbor refrains from using this option when compiling mechanism code. Complex Expressions in Current Computation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ``modcc``, Arbor's NMODL compiler, applies symbolic differentiation to the current expression to find the conductance as ``g = d I/d U`` which is then used to compute the voltage update. ``g`` is thus computed multiple times every timestep and if the corresponding expression is inefficient, it will cost more time than needed. The differentiation implementation is quite naive and will not optimise the resulting expressions. This is an internal detail of Arbor and might change in the future, but for now, this particular optimisation can help to produce better-performing code. Here is an example .. code:: : BAD, will compute m^4 * h every step i = m^4 * h * (v - e) : GOOD, will just use a constant value of g LOCAL g g = m^4 * h i = g * (v - e) Note that we do not lose accuracy here, since Arbor does not support higher-order ODEs and thus will treat ``g`` as a constant across a single timestep even if ``g`` actually depends on ``v``. Using Memory versus Computation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Commonly ion channels need to correct for temperature differences, which yields a term similar to .. code:: q = 3^(0.1*celsius - 0.63) Here, we find that the cost of the exponential when computing ``q`` in the ``DERIVATIVE`` block is high enough to make pre-computing ``q`` in ``INITIAL`` and loading the value later an optimisation. Shown below is a simplified version of this pattern from ``hh.mod`` in the Arbor sources .. code:: NEURON { ... RANGE ..., q } ASSIGNED { q } PARAMETER { ... celsius (degC) } STATE { ... } BREAKPOINT { SOLVE dS METHOD cnexp ... } INITIAL { q = 3^(0.1*celsius - 0.63) ... } DERIVATIVE states { ... : uses q } Specialised Functions ~~~~~~~~~~~~~~~~~~~~~ Some extra costs can be saved by choosing Arbor-specific optimized math functions instead of hand-rolled versions. Please consult the table in :ref:`this section `. A common pattern is the use of a guarded exponential of the form .. code:: if (x != 0) { r = a*x/(exp(x) - 1) } else { r = a } However, it can be written in Arbor's NMODL dialect as .. code:: exprelr(x) which is more efficient and has the same guarantees. NMODL files originating from NEURON often use this or related functions, e.g. ``vtrap(x, y) = y*exprelr(x/y)``. Small Tips and Micro-Optimisations ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Divisions cost a bit more than multiplications and additions. - ``m * m`` is more efficient than ``m^2``. This holds for higher powers as well and if you want to squeeze out the utmost of performance use exponentiation-by-squaring. (Although GCC does this for you. Most of the time.)